Figure 1: Histogram of Overall


Figure 2: Histogram of Shooting Rating


Figure 3: Histogram of Passing Rating


Figure 4: Histogram of Defending Rating


Figure 5: Histogram of Physicality Total


Figure 6: Histogram of Age

***

Figure 7: Histogram of Height


Figure 8: Histogram of Contract Value


Figure 9: Scatter Plot of Contract Value and Overall

***

Figure 10: Scatter Plot of Age and Overall


Figure 11: Scatter Plot of Height and Overall


Figure 12: Scatter Plot of Shooting Rating and Overall


Figure 13: Scatter Plot of Defending Rating and Overall


Figure 14: Scatter Plot of Passing Rating and Overall


Figure 15: Boxplot of Overall Rating by Position


Figure 16: Interaction Terms

## Warning: The shape palette can deal with a maximum of 6 discrete values because
## more than 6 becomes difficult to discriminate; you have 15. Consider
## specifying shapes manually if you must have them.
## Warning: Removed 2116 rows containing missing values (geom_point).


Figure 17: Building the Model Subsets

##                                                 model p   rsq   rss adjr2    cp
## 1                                            lg(VEUR) 2 0.785 47394 0.785 31497
## 2                                          A-lg(VEUR) 3 0.966  7552 0.966   997
## 3                                      A-lg(VEUR)-BPG 4 0.968  7019 0.968   590
## 4                                    A-D-lg(VEUR)-BPG 5 0.969  6790 0.969   418
## 5                              A-PsT-PhT-lg(VEUR)-BPG 6 0.970  6643 0.970   306
## 6                 A-PsT-PhT-lg(VEUR)-BPG-l(VEUR):BPCB 7 0.970  6532 0.970   224
## 7             A-I(D-PsT-PhT-lg(VEUR)-BPG-l(VEUR):BPCM 8 0.971  6471 0.971   179
## 8 A-I(D-PsT-PhT-lg(VEUR)-BPG-l(VEUR):BPCM-l(VEUR):BPG 9 0.971  6419 0.971   142
##      bic stderr
## 1  -7346   3.15
## 2 -16137   1.26
## 3 -16480   1.21
## 4 -16630   1.19
## 5 -16727   1.18
## 6 -16799   1.17
## 7 -16836   1.16
## 8 -16865   1.16
## 
## Model variables with abbreviations
##                                                                                                                                                                                            model
## lg(VEUR)                                                                                                                                                                           log(ValueEUR)
## A-lg(VEUR)                                                                                                                                                                     Age-log(ValueEUR)
## A-lg(VEUR)-BPG                                                                                                                                                  Age-log(ValueEUR)-BestPositionGK
## A-D-lg(VEUR)-BPG                                                                                                                                 Age-DefendingTotal-log(ValueEUR)-BestPositionGK
## A-PsT-PhT-lg(VEUR)-BPG                                                                                                            Age-PassingTotal-PhysicalityTotal-log(ValueEUR)-BestPositionGK
## A-PsT-PhT-lg(VEUR)-BPG-l(VEUR):BPCB                                                                  Age-PassingTotal-PhysicalityTotal-log(ValueEUR)-BestPositionGK-log(ValueEUR):BestPositionCB
## A-I(D-PsT-PhT-lg(VEUR)-BPG-l(VEUR):BPCM                                          Age-I(DefendingTotal^2)-PassingTotal-PhysicalityTotal-log(ValueEUR)-BestPositionGK-log(ValueEUR):BestPositionCM
## A-I(D-PsT-PhT-lg(VEUR)-BPG-l(VEUR):BPCM-l(VEUR):BPG Age-I(DefendingTotal^2)-PassingTotal-PhysicalityTotal-log(ValueEUR)-BestPositionGK-log(ValueEUR):BestPositionCM-log(ValueEUR):BestPositionGK
## 
## model with largest adjr2
## 8 
## 
## Number of observations
## 4791

Figure 18: VIF Scores for the Model

##              Age           Height   DefendingTotal     PassingTotal 
##         2.018873         1.955955         5.406309         4.382201 
## PhysicalityTotal    log(ValueEUR)   BestPositionCB  BestPositionCDM 
##         3.081032         3.043478         5.662960         2.206623 
##   BestPositionCF   BestPositionCM   BestPositionGK   BestPositionLB 
##         1.037259         1.635677         2.493684         1.840696 
##   BestPositionLM   BestPositionLW  BestPositionLWB   BestPositionRB 
##         1.378816         1.112406         1.241394         1.874169 
##   BestPositionRM   BestPositionRW  BestPositionRWB   BestPositionST 
##         1.644086         1.212457         1.283539         3.402799

Figure 19: Final Model

## 
## Call:
## lm(formula = Overall ~ Age + Height + DefendingTotal + I(DefendingTotal^2) + 
##     PassingTotal + PhysicalityTotal + log(ValueEUR) * BestPosition, 
##     data = fifa_smallest)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.0714 -0.6767 -0.0197  0.6420  6.0279 
## 
## Coefficients:
##                                  Estimate  Std. Error t value
## (Intercept)                   -16.5067118   0.8452714 -19.528
## Age                             0.5457429   0.0052404 104.141
## Height                         -0.0035143   0.0033896  -1.037
## DefendingTotal                 -0.0093293   0.0093857  -0.994
## I(DefendingTotal^2)             0.0001855   0.0001076   1.724
## PassingTotal                    0.0523969   0.0035790  14.640
## PhysicalityTotal                0.0251204   0.0030429   8.255
## log(ValueEUR)                   4.6208428   0.0429695 107.538
## BestPositionCB                  1.4468696   0.7637876   1.894
## BestPositionCDM                 0.7162297   0.9073359   0.789
## BestPositionCF                  7.0596134   3.9587830   1.783
## BestPositionCM                  2.0868579   0.9673519   2.157
## BestPositionGK                  4.7261300   0.7687762   6.148
## BestPositionLB                  0.4643580   1.0650687   0.436
## BestPositionLM                 -0.1970164   1.0786120  -0.183
## BestPositionLW                  3.9216465   2.8803753   1.362
## BestPositionLWB                 0.9648900   2.0280248   0.476
## BestPositionRB                  0.4388699   1.1256065   0.390
## BestPositionRM                 -2.0311614   0.9175616  -2.214
## BestPositionRW                  2.5732131   1.4765286   1.743
## BestPositionRWB                -2.3085406   1.8312908  -1.261
## BestPositionST                 -0.3106739   0.7749704  -0.401
## log(ValueEUR):BestPositionCB   -0.0666918   0.0563953  -1.183
## log(ValueEUR):BestPositionCDM  -0.0553243   0.0655927  -0.843
## log(ValueEUR):BestPositionCF   -0.5328990   0.2620185  -2.034
## log(ValueEUR):BestPositionCM   -0.1731170   0.0678564  -2.551
## log(ValueEUR):BestPositionGK   -0.2705871   0.0557554  -4.853
## log(ValueEUR):BestPositionLB   -0.0108126   0.0768752  -0.141
## log(ValueEUR):BestPositionLM    0.0237498   0.0766487   0.310
## log(ValueEUR):BestPositionLW   -0.2369725   0.2027724  -1.169
## log(ValueEUR):BestPositionLWB  -0.0387435   0.1439129  -0.269
## log(ValueEUR):BestPositionRB   -0.0086384   0.0815002  -0.106
## log(ValueEUR):BestPositionRM    0.1556315   0.0656485   2.371
## log(ValueEUR):BestPositionRW   -0.1590528   0.1047462  -1.518
## log(ValueEUR):BestPositionRWB   0.2023012   0.1308002   1.547
## log(ValueEUR):BestPositionST    0.0403280   0.0548222   0.736
##                                           Pr(>|t|)    
## (Intercept)                   < 0.0000000000000002 ***
## Age                           < 0.0000000000000002 ***
## Height                                      0.2999    
## DefendingTotal                              0.3203    
## I(DefendingTotal^2)                         0.0847 .  
## PassingTotal                  < 0.0000000000000002 ***
## PhysicalityTotal              < 0.0000000000000002 ***
## log(ValueEUR)                 < 0.0000000000000002 ***
## BestPositionCB                              0.0582 .  
## BestPositionCDM                             0.4299    
## BestPositionCF                              0.0746 .  
## BestPositionCM                              0.0310 *  
## BestPositionGK                      0.000000000851 ***
## BestPositionLB                              0.6629    
## BestPositionLM                              0.8551    
## BestPositionLW                              0.1734    
## BestPositionLWB                             0.6343    
## BestPositionRB                              0.6966    
## BestPositionRM                              0.0269 *  
## BestPositionRW                              0.0814 .  
## BestPositionRWB                             0.2075    
## BestPositionST                              0.6885    
## log(ValueEUR):BestPositionCB                0.2370    
## log(ValueEUR):BestPositionCDM               0.3990    
## log(ValueEUR):BestPositionCF                0.0420 *  
## log(ValueEUR):BestPositionCM                0.0108 *  
## log(ValueEUR):BestPositionGK        0.000001254323 ***
## log(ValueEUR):BestPositionLB                0.8882    
## log(ValueEUR):BestPositionLM                0.7567    
## log(ValueEUR):BestPositionLW                0.2426    
## log(ValueEUR):BestPositionLWB               0.7878    
## log(ValueEUR):BestPositionRB                0.9156    
## log(ValueEUR):BestPositionRM                0.0178 *  
## log(ValueEUR):BestPositionRW                0.1290    
## log(ValueEUR):BestPositionRWB               0.1220    
## log(ValueEUR):BestPositionST                0.4620    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.148 on 4755 degrees of freedom
## Multiple R-squared:  0.9716, Adjusted R-squared:  0.9714 
## F-statistic:  4646 on 35 and 4755 DF,  p-value: < 0.00000000000000022

Figure 20: Residuals vs. Fitted Plot

Figure 21: QQ Plot